Celsius scale sets the zero to the temperature of the melting ice and the 100 to the temperature of boiling ice, then it divides the mechanical dilatation of some fluid (a gas or mercury) in 100 parts and each step is one degree.
The Kelvin scale uses the same approach to divide the scale but it set up the zero to the minimum temperature that can be reached by a body (called the absolute zero).
This was selected under the idea that a minimum zero was possible when all the atoms of an object stop to move.
In reality with quantum mechanics we discovered that we cannot have an absolute zero because the particles will move under the influence of the uncertainty principle that does not allow the observer to be sure that a particle has a precise velocity (in our case zero).
Because of this, the Kelvin scale was redefined saying that the triple point of water (when it is gas, liquid and solid together) is at 273.16 degrees.
Then, because in the Celsius scale the triple point of water is at 0.01 degrees, the absolute zero of the Kelvin scale is at -273.15 Celsius.
To simplify: the zero of the Kelvin scale is more or less when the atoms are not moving and it correspond to -273.15 Celsius. The zero of the Celsius is when the ice is melting and it is at 273.15 Kelvin. Except for this shift in the scale, the everything else is the same.